Just some musings about the effect of temperature on a barrel. When a barrel is subject to some repeated closely spaced shots, the inside of the barrel heats up while the outside remains colder. In time the temperature becomes uniform and warm. The whole barrel diameter and the bore expands with the temperature. But, in the short term before equalization the bore can actually contract. The cold outer part does not let the inner part expand out, so it has to go in, and the diameter is reduced.
This differential expansion acts in the longitudinal direction too. The inside of the barrel wants to get longer, but the cooler outside does not let it. This is fine and has no major effect as long as the outside of the barrel has very uniform strength. If one side is weaker than the other then the barrel will warp, changing point of impact.
My thoughts are that hammer forged barrels are most likely to have variations in tensile strength at the outer diameter, and as a result most likely to warp with transient heating. This is because they are formed from the outside with extreme stress. The barrel actually grows 1/3 or so in length during the hammering. Further there is a move to cold forging instead of hot, which causes even more stress. Yes, they get "stress relieved", but do they really, and how uniform is it. Obviously they can't take all stress out or the steel would be no weak.
On the other hand button rifled barrels have little stress until the button rifling is done. Even then the stress is very localized and at the inside of the bore. The outside of the barrel is unaffected.
Just my musings but, my guess is that hammer forged barrels are likely the most sensitive to heating and having the point of impact "walking". Button rifled should be much more resistant, and cut rifling of course the most resistant.
Probably not an issue for hunting rifles, but in target shooting or any other application where you are looking for the best accuracy, then it may be. Could make the difference between a 1 moa barrel and a 1/4 moa one.